I stated a company when I was very young, 18 and it failed, and the next one too.  

As you said that you purchased a new home, that also guides your search.

I have a property management company that is handling this but running into issues. 

A property management company pays 15.3% self employment tax on income. 

It all depends on the market where you are, so just do a search online at what is for sale. 

My understanding is that so long as they confirm that they're moved out and give me the keys, I'm well within my rights to just have a junk remover / trash company take whatever was not there to begin with, and deduct that from the security deposit?

I’m starting to look for lenders and agents so I can narrow down my search for homes and get a good idea of what I can get. 

Do a search and you will find a ton of info on that topic.Personally this is not something I would do.

A lot of companies, entrepreneurs, people with strong family values.

This was not a new company.